German published patent application DE-OS No. 2,922,573 discloses a motor-driven chain saw wherein a tension spring is fastened to a brake band lever to allow it to pivot from the release position into a braking position. When the latching device releases the brake band lever, it is pivoted into the braking position by the tension spring. As a result, the brake band is applied to the brake drum, stopping movement of the saw chain. However, the saw chain is only slowed down upon actuation of the tripping device. When working with the motor-driven chain saw, there is the problem that the saw chain continues running for a relatively long period after the throttle is released, about 3.5 to 5 seconds. During such running down of the saw chain, there is the danger that the operator will strike the ground with the guide bar which may easily dull the saw chain and therefore require its premature replacement. In addition, particularly where space is limited, the chain saw operator may sustain injury if the guide bar accidentally touches the legs or other parts of the body.